Asymptotic Expansion of Gaussian Chaos via Probabilistic Approach

Autor:	Hashorva, Enkelejd, Korshunov, Dmitry, Piterbarg, Vladimir I.
Rok vydání:	2013
Předmět:	Mathematics - Probability 60J57 60E05 60E99
Druh dokumentu:	Working Paper
Popis:	For a centered $d$-dimensional Gaussian random vector $\xi =(\xi_1,\ldots,\xi_d)$ and a homogeneous function $h:R^d\to R$ we derive asymptotic expansions for the tail of the Gaussian chaos $h(\xi)$ given the function $h$ is sufficiently smooth. Three challenging instances of the Gaussian chaos are the determinant of a Gaussian matrix, the Gaussian orthogonal ensemble and the diameter of random Gaussian clouds. Using a direct probabilistic asymptotic method, we investigate both the asymptotic behaviour of the tail distribution of $h(\xi)$ and its density at infinity and then discuss possible extensions for some general $\xi$ with polar representation. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1307.5857 Zobrazit plný text záznamu View this record from Arxiv